Some of the very recent literature using Bayesian hierarchical models in glaciology has involved non-Gaussian assumptions at either the process, prior, or data levels. For instance, [1]} used Bayesian methods for inferring subglacial hydrological and sliding law parameters given a field of time-averaged surface velocity measurements, with application to southwestern Greenland. A physical model was constructed based on an approximate hydrostatic solution to Stokes’ equations coupled with a hydrological model. A surrogate model/emulator was used to reduce the computational complexity of running the full model numerically. Specifically, neural networks (fit using PyTorch) were chosen to learn the coefficients of basis vectors as a function of input parameters. The basis vectors were derived from a principal components analysis applied to an ensemble of computer simulator runs. The primary benefit of using the neural network emulator was to reduce the time taken to compute an approximate numerical solution to the surface velocity field. The data model used was multivariate normal, and a beta prior distribution was used for the parameters. Posterior computation was achieved with the manifold Metropolis-adjusted Langevin algorithm, a Markov chain Monte Carlo (MCMC) method that efficiently explores complex posterior distributions [2]}.
